1. Field of the Invention
The present invention relates to apparatus for resampling given information originally defined by a first series of input samples to derive a second series of output samples defining the same given information, wherein the ratio of the number of input samples of the first series to the number of output samples of the second series may be either less than or greater than unity, and, more particularly, to such apparatus suitable for use in the resizing of a video image.
2. Description of the Prior Art
For such purposes as workstation video processing, scan conversion, and scanner document preparation by means of an image scanner, it is often desirable to resample an input stream of digital-signal sample values by a predetermined improper fractional amount, in the case of signal reduction, or a predetermined proper fractional amount, in the case of signal expansion. In this regard, reference is made to the respective teachings of U.S. Pat. Nos. 4,282,546, 4,602,285 and 4,682,301.
As known in the art, the sampling of an input stream of digital-signal sample values can be altered by the fractional amount M/L by first upsampling the digital-signal sample values by a factor of L and then downsampling the upsampled digital-signal sample values by a factor of M. In order to accomplish this, relatively complex filter means, employing digital interpolation filtering subsequent to upsampling and digital low-pass prefiltering prior to downsampling, is required.
In the case of signal expansion, where M is smaller than L, there is no problem of unwanted aliasing frequencies being created by the upsampling-downsampling processing. However, in the case of signal reduction, where M is larger than L, there is a problem of unwanted aliasing frequencies being created. In order to overcome this problem, the interpolated upsampled signal must be sufficiently bandlimited by the prefiltering to prevent downsampling by an M larger than L causing aliasing. Further, the greater the amount of downsampling (i.e., the larger M is), the larger the number of kernel-function taps is required of the digital low-pass prefilter (i.e., the prefiltering must extend over many samples), thus dictating the use of a long filter response. The cost of a long filter response is added filter complexity and ultimately, silicon real estate when the filter is implemented on a VLSI chip.
In the past, the approach taken to appropriately bandlimit an image signal prior to resampling, whether upsampling, where the sample density is to be increased, or downsampling, where the sample density is to be decreased, is to prefilter the image with an adaptive 2-dimensional filter whose bandwidth is varied according to the amount of image-size reduction/expansion desired in each of the horizontal (X) dimension and vertical (Y) dimension of the image. Two types of digital filters can be used for this purpose: 1) Finite Impulse Response (FIR), or 2) Infinite Impulse Response (IIR).
FIR filters are desirable because they are guaranteed to be stable and can have linear phase--an important property in image processing. However, FIR filters do exhibit extremely long impulse responses (large number of neighborhood samples) for low-frequency filtering. Long impulse responses mean that the tails of the filters (the weighing coefficients furthest from the center filter point) have extremely small coefficients, which means that high arithmetic precision must be used. Also, long filter responses translate into many lines of data storage if used for vertical or Y-directional filtering. Both conditions of high arithmetic precision and many storage elements implies too much hardware, and thus silicon, if integrated onto an integrated circuit.
IIR filters, on the other hand, can have relatively short responses for the equivalent bandreject capability. Unfortunately, IIR filters also can be unstable and demand the use of very high arithmetic precision in computation. Also, IIR filters almost never have linear phase. One known image resizing architecture uses an IIR filter approach. Filter coefficients are updated as a function of the resizing parameter specified. This architecture requires wide dynamic range in its arithmetic in order to guarantee a stable filter for all cases. This structure also does not exhibit good bandwidth limiting for large resampling factors. This design is, therefore, not economical for silicon integration.
Except for their longer filter response, FIR filters are to be favored because they are well behaved, stable, and have linear phase. At lower spatial frequencies, the longer filter response of FIR filters presents a problem in implementation in the prior art. However, the present invention overcomes this problem.